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 left:-3.25%'>&#8226;</span></span><span style=3D'font-size:108%;color:#006=
600'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>Magnetic Flux&#13;</span></span><=
/div>
 <div style=3D'mso-line-spacing:"100 50 0";position:absolute;top:65.75%;
 left:54.3%;width:47.75%;height:5.5%'><span style=3D'position:absolute;
 top:0%;left:2.74%;width:97.25%;height:100.0%'><span style=3D'font-size:108=
%;
 color:#006600'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-2.82%'>&#8226;</span></span><span style=3D'font-size:108%;color:#006=
600'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>Induced Emf and Current&#13;</spa=
n></span></div>
 <div style=3D'mso-line-spacing:"100 50 0";position:absolute;top:74.5%;
 left:54.3%;width:41.57%;height:5.5%'><span style=3D'position:absolute;
 top:0%;left:3.15%;width:96.84%;height:100.0%'><span style=3D'font-size:108=
%;
 color:#006600'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-3.25%'>&#8226;</span></span><span style=3D'font-size:108%;color:#006=
600'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>Generators&#13;</span></span></di=
v>
 <div style=3D'mso-line-spacing:"100 50 0";position:absolute;top:83.25%;
 left:54.3%;width:41.57%;height:5.5%'><span style=3D'position:absolute;
 top:0%;left:3.15%;width:96.84%;height:100.0%'><span style=3D'font-size:108=
%;
 color:#006600'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-3.25%'>&#8226;</span></span><span style=3D'font-size:108%;color:#006=
600'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>Crossed Fields</span></span></div>
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5%;
 left:9.36%;width:83.14%;height:6.75%'>History of Magnetism</div>
 <div v:shape=3D"_x0000_s3076" class=3DO>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:16.0%;left:4.68%;width:107.3%;height:5.0%'><span style=3D'font-size:96=
%;
 color:#0000CC'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-1.04%'>&#8226;</span></span><span style=3D'font-size:96%;color:#0000=
CC'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>The first known magnets were natu=
rally
 occurring lodestones, a type <br>
  </span></span><span style=3D'position:absolute;top:21.0%;left:3.55%;width=
:104.86%;
 height:5.0%'><span style=3D'font-size:96%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>of iron ore called magnetit=
e (Fe</span><span
 style=3D'font-size:64%;color:#0000CC;position:relative;top:.37em;mso-text-=
raise:
 -25%'>3</span><span style=3D'font-size:96%;color:#0000CC'>O</span><span
 style=3D'font-size:64%;color:#0000CC;position:relative;top:.37em;mso-text-=
raise:
 -25%'>4</span><span style=3D'font-size:96%;color:#0000CC'>). People of anc=
ient
 Greece and <br>
  </span></span><span style=3D'position:absolute;top:26.0%;left:3.55%;width=
:101.87%;
 height:5.0%'><span style=3D'font-size:96%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>China discovered that a<span
 style=3D'mso-spacerun:yes'>&nbsp; </span>lodestone would always align itse=
lf in
 a <br>
  </span></span><span style=3D'position:absolute;top:31.25%;left:3.55%;
 width:108.8%;height:5.0%'><span style=3D'font-size:96%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>longitudinal direction if i=
t was
 allowed to rotate freely. This property <br>
  </span></span><span style=3D'position:absolute;top:36.25%;left:3.55%;
 width:103.93%;height:5.0%'><span style=3D'font-size:96%;color:#0000CC'><sp=
an
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>of lodestones allowed for t=
he
 creation of compasses two thousand <br>
  </span></span><span style=3D'position:absolute;top:41.5%;left:3.55%;width=
:94.0%;
 height:5.0%'><span style=3D'font-size:96%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>years ago, which was the fi=
rst
 known use of the magnet. &#13;</span></span></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:49.25%;left:4.68%;width:109.17%;height:5.0%'><span style=3D'font-size:=
96%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-1.02%'>&#8226;<=
/span></span><span
 style=3D'font-size:96%'><span style=3D'mso-spacerun:yes'>&nbsp; </span>In =
1263
 Pierre de Maricourt mapped the magnetic field of a lodestone <br>
  </span></span><span style=3D'position:absolute;top:54.25%;left:3.55%;
 width:109.55%;height:5.0%'><span style=3D'font-size:96%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>with a compass. He discover=
ed
 that a magnet had two magnetic poles <br>
  </span></span><span style=3D'position:absolute;top:59.5%;left:3.55%;width=
:94.0%;
 height:5.0%'><span style=3D'font-size:96%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>North and South poles. &#13=
;</span></span></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:67.0%;left:4.68%;width:97.37%;height:5.0%'><span style=3D'font-size:96=
%;
 color:#0000CC'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-1.15%'>&#8226;</span></span><span style=3D'font-size:96%;color:#0000=
CC'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>In the 1600's William Gilbert,
 physician of Queen Elizabeth I,<span style=3D'mso-spacerun:yes'>&nbsp;
 </span><br>
  </span></span><span style=3D'position:absolute;top:72.25%;left:3.55%;
 width:94.0%;height:5.0%'><span style=3D'font-size:96%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>concluded that Earth itself=
 is a
 giant magnet.&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:79.75%;left:4.68%;width:103.18%;height:5.0%'><span style=3D'font-size:=
96%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-1.08%'>&#8226;<=
/span></span><span
 style=3D'font-size:96%'><span style=3D'mso-spacerun:yes'>&nbsp; </span>In =
1820 the
 Danish physicist Hans Christian </span><span style=3D'mso-bidi-font-family=
:"Times New Roman";
 font-size:96%'>&Oslash;</span><span style=3D'font-size:96%'>rsted discover=
ed an
 <br>
  </span></span><span style=3D'position:absolute;top:85.0%;left:3.55%;width=
:109.92%;
 height:5.0%'><span style=3D'font-size:96%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>electric current flowing th=
rough
 a wire can cause a compass needle to <br>
  </span></span><span style=3D'position:absolute;top:90.0%;left:3.55%;width=
:96.44%;
 height:5.0%'><span style=3D'font-size:96%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>deflect, showing that magne=
tism
 and electricity were related. </span></span></div>
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.0%;
 left:8.42%;width:83.14%;height:6.75%'>History<span
 style=3D'mso-spacerun:yes'>&nbsp; </span><span style=3D'font-size:75%'>(co=
nt.)</span></div>
 <div v:shape=3D"_x0000_s225285" class=3DO>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:11.0%;left:3.74%;width:97.37%;height:4.75%'><span style=3D'font-size:9=
2%;
 color:#0000CC'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-1.15%'>&#8226;</span></span><span style=3D'font-size:92%;color:#0000=
CC'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>In 1830 Michael Faraday (British)=
 and
 Joseph Henry (American) <br>
  </span></span><span style=3D'position:absolute;top:15.75%;left:2.62%;
 width:114.23%;height:4.75%'><span style=3D'font-size:92%;color:#0000CC'><s=
pan
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>independently discovered th=
at a
 changing magnetic field produced a current <br>
  </span></span><span style=3D'position:absolute;top:20.75%;left:2.62%;
 width:112.17%;height:4.75%'><span style=3D'font-size:92%;color:#0000CC'><s=
pan
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>in a coil of wire. Faraday,=
 who
 was perhaps the greatest experimentalist of <br>
  </span></span><span style=3D'position:absolute;top:25.75%;left:2.62%;
 width:109.55%;height:4.75%'><span style=3D'font-size:92%;color:#0000CC'><s=
pan
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>all time, came up with the =
idea
 of electric and magnetic &#8220;fields.&#8221; He also <br>
  </span></span><span style=3D'position:absolute;top:30.5%;left:2.62%;width=
:113.1%;
 height:4.75%'><span style=3D'font-size:92%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>invented the dynamo (a
 generator), made major contributions to chemistry, <br>
  </span></span><span style=3D'position:absolute;top:35.5%;left:2.62%;width=
:95.69%;
 height:4.75%'><span style=3D'font-size:92%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>and invented one of the fir=
st
 electric motors&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:42.75%;left:3.74%;width:109.17%;height:4.75%'><span style=3D'font-size=
:92%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-1.02%'>&#8226;<=
/span></span><span
 style=3D'font-size:92%'><span style=3D'mso-spacerun:yes'>&nbsp; </span>In =
the 19th
 century James Clerk Maxwell, a Scottish physicist and one of <br>
  </span></span><span style=3D'position:absolute;top:47.5%;left:2.62%;width=
:111.79%;
 height:4.75%'><span style=3D'font-size:92%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>the great theoreticians of =
all
 times, mathematically unified the electric and <br>
  </span></span><span style=3D'position:absolute;top:52.5%;left:2.62%;width=
:113.48%;
 height:4.75%'><span style=3D'font-size:92%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>magnetic forces. He also pr=
oposed
 that light was electromagnetic radiation.</span><span style=3D'font-size:9=
2%;
 color:#0000CC'> &#13;</span></span></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:59.75%;left:3.74%;width:106.55%;height:4.75%'><span style=3D'font-size=
:92%;
 color:#0000CC'><span style=3D'mso-special-format:bullet;position:absolute;
 left:-1.05%'>&#8226;</span></span><span style=3D'font-size:92%;color:#0000=
CC'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>In the late 19</span><span
 style=3D'font-size:61%;color:#0000CC;position:relative;top:-.45em;mso-text=
-raise:
 30%'>th</span><span style=3D'font-size:92%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>century Pierre Curie discovered th=
at
 magnets loose their <br>
  </span></span><span style=3D'position:absolute;top:64.75%;left:2.62%;
 width:106.74%;height:4.75%'><span style=3D'font-size:92%;color:#0000CC'><s=
pan
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>magnetism above a certain
 temperature that later became known as the <br>
  </span></span><span style=3D'position:absolute;top:69.5%;left:2.62%;width=
:95.69%;
 height:4.75%'><span style=3D'font-size:92%;color:#0000CC'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>Curie point.&#13;</span></s=
pan></div>
 <div style=3D'mso-line-spacing:"100 50 0"'><span style=3D'position:absolut=
e;
 top:77.0%;left:3.74%;width:107.49%;height:4.75%'><span style=3D'font-size:=
92%'><span
 style=3D'mso-special-format:bullet;position:absolute;left:-1.04%'>&#8226;<=
/span></span><span
 style=3D'font-size:92%'><span style=3D'mso-spacerun:yes'>&nbsp; </span>In =
the
 1900's scientists discover superconductivity. Superconductors are <br>
  </span></span><span style=3D'position:absolute;top:81.75%;left:2.62%;
 width:106.36%;height:4.75%'><span style=3D'font-size:92%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>materials that have a zero
 resistance to a current flowing through them <br>
  </span></span><span style=3D'position:absolute;top:86.75%;left:2.62%;
 width:108.8%;height:4.75%'><span style=3D'font-size:92%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>when they are a very low
 temperature. They also exclude magnetic field <br>
  </span></span><span style=3D'position:absolute;top:91.5%;left:2.62%;width=
:104.49%;
 height:4.75%'><span style=3D'font-size:92%'><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>lines (the Meissner effect)=
 which
 makes magnetic levitation possible.</span></span></div>
 </div>
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0%;
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r'>Magnetic
 Dipoles</span></div>
 <div v:shape=3D"_x0000_s53251" class=3DO style=3D'mso-line-spacing:"100 50=
 0"'><span
 style=3D'position:absolute;top:12.0%;left:3.55%;width:59.55%;height:5.25%'=
>Recall
 that an electric dipole consists </span><span style=3D'position:absolute;
 top:17.5%;left:3.55%;width:54.11%;height:5.25%'>of two equal but opposite
 charges </span><span style=3D'position:absolute;top:22.75%;left:3.55%;
 width:61.61%;height:5.25%'>separated by some distance, such as in </span><=
span
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>a
 polar molecule. Every magnet is a </span><span style=3D'position:absolute;
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net
 is a </span><span style=3D'position:absolute;top:38.75%;left:3.55%;width:6=
0.86%;
 height:5.25%'>simple example. Note how the <span style=3D'font-family:Aria=
l'><b><i>E</i></b></span>
 field </span><span style=3D'position:absolute;top:44.0%;left:3.55%;width:5=
7.67%;
 height:5.25%'>due an electric dipole is just like the </span><span
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 field (<span style=3D'font-family:Arial'><b><i>B</i></b></span> field) of =
a bar </span><span
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 Field lines emanate from the </span><span style=3D'position:absolute;top:6=
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an
 style=3D'mso-spacerun:yes'>&nbsp; </span><span style=3D'font-size:117%'><b=
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the
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6.17%;
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ly:
 Arial'><b><i>E</i></b></span> </span><span style=3D'position:absolute;
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5%'><span
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0"'><span
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'>We
 have studied electric fields to due isolated <b>+</b> or<span
 style=3D'mso-spacerun:yes'>&nbsp; </span><span style=3D'font-size:117%'><b=
>-</b></span><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>charges, but as </span><span
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%'>far
 as we know, magnetic monopole do not exist, meaning it is </span><span
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'>impossible
 to isolate a N or S pole. The bar magnet on the left is </span><span
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'>surrounded
 by iron filings, which orient themselves according to the </span><span
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%'>magnetic
 field they are in. When we try to separate the two poles by </span><span
 style=3D'position:absolute;top:86.5%;left:3.55%;width:102.24%;height:5.25%=
'>breaking
 the magnet, we only succeed in producing two distinct </span><span
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'>dipoles
 (pic on right).</span></div>
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  location=3D"Bar magnet demo"
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<a
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 <div v:shape=3D"_x0000_s193540" class=3DT style=3D'position:absolute;top:8=
.5%;
 left:7.67%;width:83.14%;height:6.75%'>Magnetic Fields</div>
 <div v:shape=3D"_x0000_s193541" class=3DO style=3D'mso-line-spacing:"100 5=
0 0"'><span
 style=3D'position:absolute;top:18.75%;left:5.99%;width:106.36%;height:5.25=
%'>You
 have seen that electric fields and be uniform, nonuniform and </span><span
 style=3D'position:absolute;top:24.0%;left:5.99%;width:102.62%;height:5.25%=
'>symmetric,
 or nonuniform and asymmetric. The same is true for </span><span
 style=3D'position:absolute;top:29.5%;left:5.99%;width:91.57%;height:5.25%'=
>magnetic
 fields. (Later we&#8217;ll see how to produce uniform </span><span
 style=3D'position:absolute;top:34.75%;left:5.99%;width:97.75%;height:5.25%=
'>magnetic
 fields with a current flowing through a coil called a </span><span
 style=3D'position:absolute;top:40.0%;left:5.99%;width:103.55%;height:5.25%=
'>solenoid.)
 Regardless of symmetry or complexity, the SI unit for </span><span
 style=3D'position:absolute;top:45.25%;left:5.99%;width:105.61%;height:5.25=
%'>any
 <span style=3D'font-family:Arial'><b><i>E</i></b></span> field is the N/C,=
 since
 by definition an electric field is force </span><span style=3D'position:ab=
solute;
 top:50.74%;left:5.99%;width:103.55%;height:5.25%'>per unit charge. Because
 there are no magnetic monopoles, there </span><span style=3D'position:abso=
lute;
 top:56.0%;left:5.99%;width:90.44%;height:5.25%'>is no analogous definition=
 for
 <span style=3D'font-family:Arial'><b><i>B</i></b></span>. However, regardl=
ess of
 </span><span style=3D'position:absolute;top:61.25%;left:5.99%;width:104.86=
%;
 height:5.25%'>symmetry or complexity, there is only one SI unit for a <span
 style=3D'font-family:Arial'><b><i>B</i></b></span> field. It </span><span
 style=3D'position:absolute;top:66.75%;left:5.99%;width:103.93%;height:5.25=
%'>is
 called a tesla and its symbol is T. The coming slides will show </span><sp=
an
 style=3D'position:absolute;top:72.0%;left:5.99%;width:104.49%;height:5.25%=
'>how
 to write a tesla in terms of other SI units. The magnetic field </span><sp=
an
 style=3D'position:absolute;top:77.25%;left:5.99%;width:105.05%;height:5.25=
%'>vector
 is always tangent to the magnetic field. Unlike <span style=3D'font-family=
:Arial'><b><i>E</i></b></span>
 fields, all </span><span style=3D'position:absolute;top:82.75%;left:5.99%;
 width:105.43%;height:5.25%'>magnetic field lines that come from the N pole
 must land on the S </span><span style=3D'position:absolute;top:88.0%;left:=
5.99%;
 width:88.95%;height:5.25%'>pole--no field lines go to or come from infinit=
y.</span></div>
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ition:absolute;
  left:30pt;top:5in;width:9in;height:93.5pt' filled=3D"f" fillcolor=3D"#0c9=
 [4]"
  stroked=3D"f" strokecolor=3D"black [1]">
  <v:fill color2=3D"white [0]"/>
  <v:shadow color=3D"gray [2]"/>
  <v:textbox style=3D'mso-fit-shape-to-text:t'/>
 </v:shape><v:rect id=3D"_x0000_s58377" style=3D'position:absolute;left:36p=
t;top:492pt;
  width:654pt;height:36pt' filled=3D"f" fillcolor=3D"#0c9 [4]" stroked=3D"f"
  strokecolor=3D"black [1]">
  <v:fill color2=3D"white [0]"/>
  <v:shadow color=3D"gray [2]"/>
  <v:textbox style=3D'mso-fit-shape-to-text:t'/>
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 <div v:shape=3D"_x0000_s58370" class=3DT style=3D'position:absolute;top:5.=
25%;
 left:8.42%;width:83.14%;height:6.75%'><span style=3D'font-family:Westminst=
er'>Force
 Due to Magnetic Field</span></div>
 <div v:shape=3D"_x0000_s58371" class=3DO style=3D'mso-line-spacing:"100 50=
 0"'><span
 style=3D'position:absolute;top:30.0%;left:9.36%;width:80.71%;height:5.25%'=
><span
 style=3D'mso-special-format:lastCR;display:none'>&#13;</span></span></div>
 <div v:shape=3D"_x0000_s58372" class=3DO style=3D'mso-line-spacing:"100 50=
 0"'><span
 style=3D'position:absolute;top:14.24%;left:4.3%;width:108.05%;height:5.25%=
'>The
 force exerted on a charged particle by a magnetic field is given </span><s=
pan
 style=3D'position:absolute;top:19.75%;left:4.3%;width:92.32%;height:5.25%'=
>by
 the vector cross product: </span></div>
 <div v:shape=3D"_x0000_s58373" class=3DO style=3D'mso-line-spacing:"100 50=
 0";
 position:absolute;top:84.0%;left:37.64%;width:44.75%;height:7.5%'><span
 style=3D'font-family:Arial;font-size:133%;color:red'><i>F =3D q</i></span>=
<span
 style=3D'font-family:Arial;font-size:42%;color:red'><i> </i></span><span
 style=3D'font-family:Arial;font-size:133%;color:red'><i>v</i></span><span
 style=3D'font-family:Arial;font-size:42%;color:red'><i> </i></span><span
 style=3D'font-family:Arial;font-size:133%;color:red'><i>B</i></span><span
 style=3D'font-family:Arial;font-size:42%;color:red'><i> </i></span><span
 style=3D'font-family:Arial;font-size:133%;color:red'>sin</span><span
 style=3D'font-family:Symbol;mso-ascii-font-family:Arial;font-size:133%;
 color:red;mso-char-type:symbol'><i>q</i></span><span style=3D'font-family:=
Arial;
 font-size:133%;color:red'><i> </i></span></div>
 <div v:shape=3D"_x0000_s58374" class=3DO>
 <div style=3D'mso-line-spacing:"100 50 0";position:absolute;top:35.25%;
 left:5.24%;width:81.46%;height:5.25%'><span style=3D'font-family:Arial;
 color:#9900FF'><b><i>F</i></b></span><span style=3D'color:#9900FF'> =3D fo=
rce
 (vector)&#13;</span></div>
 <div style=3D'mso-line-spacing:"100 50 0";position:absolute;top:43.25%;
 left:5.24%;width:81.46%;height:5.25%'><span style=3D'font-family:Arial;
 color:#9900FF'><i>q</i></span><span style=3D'color:#9900FF'> =3D charge on=
 the
 particle (scalar)&#13;</span></div>
 <div style=3D'mso-line-spacing:"100 50 0";position:absolute;top:51.24%;
 left:5.24%;width:81.64%;height:5.25%'><span style=3D'font-family:Arial;
 color:#9900FF'><b><i>v</i></b></span><span style=3D'color:#9900FF'> =3D ve=
locity
 of the particle relative to field (vector)&#13;</span></div>
 <div style=3D'mso-line-spacing:"100 50 0";position:absolute;top:59.25%;
 left:5.24%;width:81.46%;height:5.25%'><span style=3D'font-family:Arial;
 color:#9900FF'><b><i>B</i></b></span><span style=3D'color:#9900FF'> =3D ma=
gnetic
 field (vector)</span></div>
 </div>
 <div v:shape=3D"_x0000_s58375" class=3DO style=3D'mso-line-spacing:"100 50=
 0";
 position:absolute;top:26.75%;left:38.57%;width:44.75%;height:7.75%'><span
 style=3D'font-family:Arial;font-size:150%;color:red'><b><i>F</i></b></span=
><span
 style=3D'font-family:Arial;font-size:150%;color:red'><i> =3D q</i></span><=
span
 style=3D'font-family:Arial;font-size:50%;color:red'><i> </i></span><span
 style=3D'font-family:Arial;font-size:150%;color:red'><b><i>v</i></b></span=
><span
 style=3D'font-family:Arial;font-size:75%;color:red'><i> </i></span><span
 style=3D'font-family:Symbol;mso-ascii-font-family:Arial;font-size:133%;
 color:red;mso-char-type:symbol'>&acute;</span><span style=3D'font-family:A=
rial;
 font-size:50%;color:red'><i> </i></span><span style=3D'font-family:Arial;
 font-size:150%;color:red'><b><i>B</i></b></span><span style=3D'font-family=
:Arial;
 font-size:150%;color:red;mso-special-format:lastCR;display:none'><b><i>&#1=
3;</i></b></span></div>
 <div v:shape=3D"_x0000_s58376" class=3DO style=3D'mso-line-spacing:"100 50=
 0"'><span
 style=3D'position:absolute;top:67.75%;left:5.24%;width:90.44%;height:5.25%=
'>Recall
 that the magnitude of a cross is the product of the </span><span
 style=3D'position:absolute;top:73.0%;left:5.24%;width:98.5%;height:5.25%'>=
magnitudes
 of the vectors times the sine of the angle between </span><span
 style=3D'position:absolute;top:78.25%;left:5.24%;width:92.69%;height:5.25%=
'>them.
 So, the magnitude of the magnetic force is given by</span></div>
 <div v:shape=3D"_x0000_s58377" class=3DO style=3D'mso-line-spacing:"100 50=
 0";
 position:absolute;top:91.75%;left:5.99%;width:88.95%;height:5.75%'>where<s=
pan
 style=3D'mso-spacerun:yes'>&nbsp; </span><span style=3D'font-family:Symbol;
 mso-char-type:symbol'><i>q</i></span><span style=3D'mso-spacerun:yes'>&nbs=
p;
 </span>is angle between <span style=3D'font-family:Arial'><i>q</i></span><=
span
 style=3D'font-family:Arial;font-size:42%'><i> </i></span><span style=3D'fo=
nt-family:
 Arial'><b><i>v</i></b></span> and<span style=3D'mso-spacerun:yes'>&nbsp; <=
/span><span
 style=3D'font-family:Arial'><b><i>B</i></b></span><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>vectors.</div>
</p:slide></div>

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 <div v:shape=3D"_x0000_s191490" class=3DT style=3D'position:absolute;top:5=
.25%;
 left:8.42%;width:83.14%;height:6.75%'>Cross Product Review<span
 lang=3DES-MODERN style=3D'mso-special-format:lastCR;display:none'>&#13;</s=
pan></div>
 <div v:shape=3D"_x0000_s191491" class=3DO style=3D'position:absolute;top:1=
2.75%;
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pan><span
 style=3D'font-family:Arial;font-size:117%'> </span><span style=3D'font-fam=
ily:
 Arial;font-size:58%'> </span><span style=3D'font-family:Arial;font-size:11=
7%;
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%'><b>1</b></span><span
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ily:Symbol;
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pan
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ial;
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%'>1</span><span
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 style=3D'font-family:Arial;font-size:117%;color:#000099'><i>z</i></span><s=
pan
 style=3D'font-family:Arial;font-size:78%;color:#000099;position:relative;
 top:.37em;mso-text-raise:-25%'>1</span><span style=3D'font-family:Arial;
 font-size:58%;color:#000099'><span style=3D'mso-spacerun:yes'>&nbsp;</span=
></span><span
 style=3D'font-family:Symbol;mso-ascii-font-family:Arial;font-size:150%;
 color:#000099;mso-char-type:symbol'><b>&ntilde;</b></span><span
 lang=3DES-MODERN style=3D'font-family:Arial;font-size:117%;color:#000099;
 mso-special-format:lastCR;display:none'>&#13;</span></div>
 <div v:shape=3D"_x0000_s191492" class=3DO style=3D'position:absolute;top:1=
3.0%;
 left:41.38%;width:42.69%;height:8.5%'><span style=3D'font-size:117%'>and</=
span><span
 style=3D'font-family:Arial;font-size:117%;color:blue;mso-color-index:6'> <=
/span><span
 style=3D'font-family:Arial;font-size:58%;color:blue;mso-color-index:6'> </=
span><span
 style=3D'font-family:Arial;font-size:117%;color:red'><b><i>v</i></b></span=
><span
 style=3D'font-family:Arial;font-size:78%;color:red;position:relative;top:.=
37em;
 mso-text-raise:-25%'><b>2</b></span><span style=3D'font-family:Arial;font-=
size:
 117%;color:red'><span style=3D'mso-spacerun:yes'>&nbsp;</span>=3D </span><=
span
 style=3D'font-family:Symbol;mso-ascii-font-family:Arial;font-size:150%;
 color:red;mso-char-type:symbol'><b>&aacute;</b></span><span style=3D'font-=
family:
 Arial;font-size:58%;color:red'> </span><span style=3D'font-family:Arial;
 font-size:117%;color:red'><i>x</i></span><span style=3D'font-family:Arial;
 font-size:78%;color:red;position:relative;top:.37em;mso-text-raise:-25%'>2=
</span><span
 style=3D'font-family:Arial;font-size:117%;color:red'>, </span><span
 style=3D'font-family:Arial;font-size:117%;color:red'><i>y</i></span><span
 style=3D'font-family:Arial;font-size:78%;color:red;position:relative;top:.=
37em;
 mso-text-raise:-25%'>2</span><span style=3D'font-family:Arial;font-size:11=
7%;
 color:red'>, </span><span style=3D'font-family:Arial;font-size:117%;color:=
red'><i>z</i></span><span
 style=3D'font-family:Arial;font-size:78%;color:red;position:relative;top:.=
37em;
 mso-text-raise:-25%'>2</span><span style=3D'font-family:Arial;font-size:58=
%;
 color:red'><span style=3D'mso-spacerun:yes'>&nbsp;</span></span><span
 style=3D'font-family:Symbol;mso-ascii-font-family:Arial;font-size:150%;
 color:red;mso-char-type:symbol'><b>&ntilde;</b></span><span style=3D'font-=
family:
 Arial;font-size:133%'>.</span><span lang=3DES-MODERN style=3D'font-family:=
Arial;
 mso-special-format:lastCR;display:none'>&#13;</span></div>
 <div v:shape=3D"_x0000_s191493" class=3DO style=3D'mso-line-spacing:"100 5=
0 0"'><span
 style=3D'position:absolute;top:17.75%;left:5.24%;width:94.75%;height:5.25%=
'><br>
  </span><span style=3D'position:absolute;top:23.0%;left:5.24%;width:104.49=
%;
 height:5.25%'>By definition, the cross product of these vectors (pronounced
 &#8220;<span style=3D'font-family:Arial'><b><i>v</i></b></span><span
 style=3D'font-family:Arial;font-size:67%;position:relative;top:.37em;mso-t=
ext-raise:
 -25%'>1</span><b><span style=3D'mso-spacerun:yes'>&nbsp;</span></b><span
 style=3D'font-size:50%'><b><span style=3D'mso-spacerun:yes'>&nbsp;</span><=
/b></span></span><span
 style=3D'position:absolute;top:28.24%;left:5.24%;width:94.75%;height:5.25%=
'>cross<b>
 </b><span style=3D'font-size:50%'><b> </b></span><span style=3D'font-famil=
y:Arial'><b><i>v</i></b></span><span
 style=3D'font-family:Arial;font-size:67%;position:relative;top:.37em;mso-t=
ext-raise:
 -25%'>2</span>&#8221;) is given by the following determinant.<span
 style=3D'mso-spacerun:yes'>&nbsp; </span><span lang=3DES-MODERN style=3D'm=
so-special-format:
 lastCR;display:none'>&#13;</span></span></div>
 <div v:shape=3D"_x0000_s191495" class=3DO style=3D'mso-line-spacing:"100 5=
0 0";
 position:absolute;top:45.0%;left:25.28%;width:18.53%;height:7.5%'><span
 style=3D'font-family:Arial;font-size:117%;color:#000099'><b><i>v</i></b></=
span><span
 style=3D'font-family:Arial;font-size:78%;color:#000099;position:relative;
 top:.37em;mso-text-raise:-25%'><b>1</b></span><span style=3D'font-family:A=
rial;
 font-size:117%'><b><span style=3D'mso-spacerun:yes'>&nbsp;</span></b></spa=
n><span
 style=3D'font-family:Symbol;mso-ascii-font-family:Arial;font-size:133%;
 mso-char-type:symbol'><b>&acute;</b></span><span style=3D'font-family:Aria=
l;
 font-size:117%'><b> </b></span><span style=3D'font-family:Arial;font-size:=
117%;
 color:red'><b><i>v</i></b></span><span style=3D'font-family:Arial;font-siz=
e:
 78%;color:red;position:relative;top:.37em;mso-text-raise:-25%'><b>2</b></s=
pan><span
 style=3D'font-family:Arial;font-size:78%;position:relative;top:.37em;mso-t=
ext-raise:
 -25%'><b><span style=3D'mso-spacerun:yes'>&nbsp;</span></b></span><span
 style=3D'font-family:Arial;font-size:33%;position:relative;top:.37em;mso-t=
ext-raise:
 -25%'><b><span style=3D'mso-spacerun:yes'>&nbsp;</span></b></span><span
 style=3D'font-family:Arial;font-size:117%'>=3D</span><span style=3D'font-f=
amily:
 Arial;font-size:117%'><span style=3D'mso-spacerun:yes'>&nbsp; </span></spa=
n><span
 lang=3DES-MODERN style=3D'font-family:Arial;font-size:117%;mso-special-for=
mat:
 lastCR;display:none'>&#13;</span></div>
 <div v:shape=3D"_x0000_s191498" class=3DO style=3D'position:absolute;top:4=
6.5%;
 left:43.82%;width:20.97%;height:6.0%'><span style=3D'font-family:Arial;
 font-size:58%;color:#000099'><span style=3D'mso-spacerun:yes'>&nbsp;</span=
></span><span
 style=3D'font-family:Arial;font-size:117%;color:#000099'><i>x</i></span><s=
pan
 style=3D'font-family:Arial;font-size:78%;color:#000099;position:relative;
 top:.37em;mso-text-raise:-25%'>1</span><span style=3D'font-family:Arial;
 font-size:117%;color:#000099'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;
 </span></span><span style=3D'font-family:Arial;font-size:117%;color:#00009=
9'><i>y</i></span><span
 style=3D'font-family:Arial;font-size:78%;color:#000099;position:relative;
 top:.37em;mso-text-raise:-25%'>1</span><span style=3D'font-family:Arial;
 font-size:117%;color:#000099'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;
 </span></span><span style=3D'font-family:Arial;font-size:117%;color:#00009=
9'><i>z</i></span><span
 style=3D'font-family:Arial;font-size:78%;color:#000099;position:relative;
 top:.37em;mso-text-raise:-25%'>1</span><span style=3D'font-family:Arial;
 font-size:58%;color:#000099'><span style=3D'mso-spacerun:yes'>&nbsp;</span=
></span><span
 lang=3DES-MODERN style=3D'font-family:Arial;font-size:117%;color:#000099;
 mso-special-format:lastCR;display:none'>&#13;</span></div>
 <div v:shape=3D"_x0000_s191499" class=3DO style=3D'position:absolute;top:5=
4.5%;
 left:43.63%;width:20.97%;height:6.0%'><span style=3D'font-family:Arial;
 font-size:58%;color:red'><span style=3D'mso-spacerun:yes'>&nbsp;</span></s=
pan><span
 style=3D'font-family:Arial;font-size:117%;color:red'><i>x</i></span><span
 style=3D'font-family:Arial;font-size:78%;color:red;position:relative;top:.=
37em;
 mso-text-raise:-25%'>2</span><span style=3D'font-family:Arial;font-size:11=
7%;
 color:red'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span></span><sp=
an
 style=3D'font-family:Arial;font-size:117%;color:red'><i>y</i></span><span
 style=3D'font-family:Arial;font-size:78%;color:red;position:relative;top:.=
37em;
 mso-text-raise:-25%'>2</span><span style=3D'font-family:Arial;font-size:11=
7%;
 color:red'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span></span><sp=
an
 style=3D'font-family:Arial;font-size:117%;color:red'><i>z</i></span><span
 style=3D'font-family:Arial;font-size:78%;color:red;position:relative;top:.=
37em;
 mso-text-raise:-25%'>2</span><span style=3D'font-family:Arial;font-size:58=
%;
 color:red'><span style=3D'mso-spacerun:yes'>&nbsp;</span></span><span
 lang=3DES-MODERN style=3D'font-family:Arial;font-size:117%;color:red;mso-s=
pecial-format:
 lastCR;display:none'>&#13;</span></div>
 <div v:shape=3D"_x0000_s191500" class=3DO style=3D'position:absolute;top:3=
8.5%;
 left:44.38%;width:20.59%;height:6.0%'><span style=3D'font-family:Arial;
 font-size:58%;color:#000099'><b><span style=3D'mso-spacerun:yes'>&nbsp;</s=
pan></b></span><span
 style=3D'font-family:Arial;font-size:117%'><b>i<span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp; </span></b></span><span
 style=3D'font-size:117%'><b>j</b></span><span style=3D'font-family:Arial;
 font-size:117%'><b><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbs=
p;
 </span>k</b></span><span style=3D'font-family:Arial;font-size:58%;color:#0=
00099'><b>
 </b></span><span lang=3DES-MODERN style=3D'font-family:Arial;font-size:117=
%;
 color:#000099;mso-special-format:lastCR;display:none'><b>&#13;</b></span><=
/div>
 <div v:shape=3D"_x0000_s191502" class=3DO style=3D'mso-line-spacing:"100 5=
0 0";
 position:absolute;top:65.5%;left:6.17%;width:98.87%;height:6.75%'><span
 style=3D'font-family:Arial;font-size:117%'><i>=3D </i></span><span
 style=3D'font-family:Arial;font-size:117%'>(</span><span style=3D'font-fam=
ily:
 Arial;font-size:117%;color:#000099'><i>y</i></span><span style=3D'font-fam=
ily:
 Arial;font-size:78%;color:#000099;position:relative;top:.37em;mso-text-rai=
se:
 -25%'>1</span><span style=3D'font-family:Arial;font-size:58%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></i></span><span style=3D'font-fam=
ily:
 Arial;font-size:117%;color:red'><i>z</i></span><span style=3D'font-family:=
Arial;
 font-size:78%;color:red;position:relative;top:.37em;mso-text-raise:-25%'>2=
</span><span
 style=3D'font-family:Arial;font-size:117%;color:red'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></i></span><span style=3D'font-fam=
ily:
 Arial;font-size:117%'><i>- </i></span><span style=3D'font-family:Arial;
 font-size:117%;color:red'><i>y</i></span><span style=3D'font-family:Arial;
 font-size:78%;color:red;position:relative;top:.37em;mso-text-raise:-25%'>2=
</span><span
 style=3D'font-family:Arial;font-size:58%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></i></span><span style=3D'font-fam=
ily:
 Arial;font-size:117%;color:#000099'><i>z</i></span><span style=3D'font-fam=
ily:
 Arial;font-size:78%;color:#000099;position:relative;top:.37em;mso-text-rai=
se:
 -25%'>1</span><span style=3D'font-family:Arial;font-size:117%'>)</span><sp=
an
 style=3D'font-family:Arial;font-size:42%'> </span><span style=3D'font-fami=
ly:Arial;
 font-size:117%'><b>i</b></span><span style=3D'font-family:Arial;font-size:=
117%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp; </span></i></span><span style=3D'font-fa=
mily:
 Arial;font-size:133%'>-</span><span style=3D'font-family:Arial;font-size:1=
17%'><i>
 </i></span><span style=3D'font-family:Arial;font-size:58%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></i></span><span style=3D'font-fam=
ily:
 Arial;font-size:117%'>(</span><span style=3D'font-family:Arial;font-size:1=
17%;
 color:#000099'><i>x</i></span><span style=3D'font-family:Arial;font-size:7=
8%;
 color:#000099;position:relative;top:.37em;mso-text-raise:-25%'>1</span><sp=
an
 style=3D'font-family:Arial;font-size:58%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></i></span><span style=3D'font-fam=
ily:
 Arial;font-size:117%;color:red'><i>z</i></span><span style=3D'font-family:=
Arial;
 font-size:78%;color:red;position:relative;top:.37em;mso-text-raise:-25%'>2=
</span><span
 style=3D'font-family:Arial;font-size:117%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>- </i></span><span style=3D'font-f=
amily:
 Arial;font-size:117%;color:red'><i>x</i></span><span style=3D'font-family:=
Arial;
 font-size:78%;color:red;position:relative;top:.37em;mso-text-raise:-25%'>2=
</span><span
 style=3D'font-family:Arial;font-size:58%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></i></span><span style=3D'font-fam=
ily:
 Arial;font-size:117%;color:#000099'><i>z</i></span><span style=3D'font-fam=
ily:
 Arial;font-size:78%;color:#000099;position:relative;top:.37em;mso-text-rai=
se:
 -25%'>1</span><span style=3D'font-family:Arial;font-size:117%'>)</span><sp=
an
 style=3D'font-family:Arial;font-size:42%'> </span><span style=3D'font-size=
:117%'><b>j</b></span><span
 style=3D'font-family:Arial;font-size:117%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>+ </i></span><span style=3D'font-=
family:
 Arial;font-size:117%'>(</span><span style=3D'font-family:Arial;font-size:1=
17%;
 color:#000099'><i>x</i></span><span style=3D'font-family:Arial;font-size:7=
8%;
 color:#000099;position:relative;top:.37em;mso-text-raise:-25%'>1</span><sp=
an
 style=3D'font-family:Arial;font-size:58%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></i></span><span style=3D'font-fam=
ily:
 Arial;font-size:117%;color:red'><i>y</i></span><span style=3D'font-family:=
Arial;
 font-size:78%;color:red;position:relative;top:.37em;mso-text-raise:-25%'>2=
</span><span
 style=3D'font-family:Arial;font-size:117%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span>- </i></span><span style=3D'font-f=
amily:
 Arial;font-size:117%;color:red'><i>x</i></span><span style=3D'font-family:=
Arial;
 font-size:78%;color:red;position:relative;top:.37em;mso-text-raise:-25%'>2=
</span><span
 style=3D'font-family:Arial;font-size:58%'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></i></span><span style=3D'font-fam=
ily:
 Arial;font-size:117%;color:#000099'><i>y</i></span><span style=3D'font-fam=
ily:
 Arial;font-size:78%;color:#000099;position:relative;top:.37em;mso-text-rai=
se:
 -25%'>1</span><span style=3D'font-family:Arial;font-size:117%'>)</span><sp=
an
 style=3D'font-family:Arial;font-size:42%'> </span><span style=3D'font-fami=
ly:Arial;
 font-size:117%'><b>k</b></span><span lang=3DES-MODERN style=3D'font-family=
:Arial;
 font-size:117%;mso-special-format:lastCR;display:none'><b>&#13;</b></span>=
</div>
 <div v:shape=3D"_x0000_s191503" class=3DO style=3D'mso-line-spacing:"100 5=
0 0"'><span
 style=3D'position:absolute;top:75.75%;left:5.24%;width:104.11%;height:5.25=
%'>Note
 that the cross product of two vectors is a vector itself that is </span><s=
pan
 style=3D'position:absolute;top:80.5%;left:5.24%;width:101.31%;height:5.75%=
'><span
 style=3D'font-family:Symbol;mso-char-type:symbol'>^</span> to each of the
 original vectors.<span style=3D'mso-spacerun:yes'>&nbsp; </span><b>i</b>, =
<b>j</b>,
 and <b>k</b> are the unit vectors </span><span style=3D'position:absolute;
 top:86.25%;left:5.24%;width:105.8%;height:5.25%'>pointing, along the posit=
ive
 x, y, and z axes, respectively. (See the </span><span style=3D'position:ab=
solute;
 top:91.75%;left:5.24%;width:89.7%;height:5.25%'>vector presentation for a
 review of determinants.)<span lang=3DES-MODERN style=3D'mso-special-format=
:lastCR;
 display:none'>&#13;</span></span></div>
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k;
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;</b></span><span
 style=3D'font-size:133%'><b><i> </i></b></span><span style=3D'font-family:=
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0 0"'><span
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>A
 quick way to determine the direction of a cross product is to </span><span
 style=3D'position:absolute;top:20.25%;left:3.93%;width:99.62%;height:7.0%'=
>use
 the right hand rule. To find <span style=3D'font-size:42%'><span
 style=3D'mso-spacerun:yes'>&nbsp;</span></span><span style=3D'font-size:12=
5%'><b><i>a</i></b></span><span
 style=3D'font-size:117%'> </span><span style=3D'font-family:Symbol;font-si=
ze:125%;
 mso-char-type:symbol'><b>&acute;</b></span><span style=3D'font-size:83%'><=
b> </b></span><span
 style=3D'font-family:Arial;font-size:117%'><b><i>b</i></b></span>, place t=
he
 knife edge of </span><span style=3D'position:absolute;top:27.5%;left:3.93%;
 width:102.62%;height:6.5%'>your right hand (pinky side) along <span
 style=3D'font-size:42%'><span style=3D'mso-spacerun:yes'>&nbsp;</span></sp=
an><span
 style=3D'font-size:125%'><b><i>a </i></b></span><span style=3D'font-size:4=
2%'><b><i>
 </i></b></span>and curl your hand toward <span style=3D'font-size:42%'><sp=
an
 style=3D'mso-spacerun:yes'>&nbsp;</span></span></span><span style=3D'posit=
ion:
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en
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span></span></div>
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0 0";
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 proven that the magnitude of<span style=3D'font-family:Arial'> </span><span
 lang=3DES-MODERN style=3D'font-family:Arial;mso-special-format:lastCR;disp=
lay:
 none'>&#13;</span></div>
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0 0";
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 by:<span lang=3DES-MODERN style=3D'mso-special-format:lastCR;display:none'=
>&#13;</span></div>
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0 0";
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 font-size:38%'><i> </i></span><span style=3D'font-family:Arial;font-size:1=
33%'><i>b</i></span><span
 style=3D'font-family:Arial;font-size:38%'> </span><span style=3D'font-fami=
ly:Arial;
 font-size:133%'>sin</span><span style=3D'font-family:Symbol;mso-ascii-font=
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0 0"'><span
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/span><span
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size:
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 </v:shape>
 <div v:shape=3D"_x0000_s8194" class=3DT style=3D'position:absolute;top:7.7=
5%;
 left:8.42%;width:83.14%;height:6.0%'><span style=3D'font-family:Westminste=
r;
 font-size:88%'>Magnetic Field Units</span></div>
 <div v:shape=3D"_x0000_s8198" class=3DO style=3D'mso-line-spacing:"100 20 =
0"'><span
 style=3D'position:absolute;top:74.25%;left:7.67%;width:98.5%;height:5.25%'=
>A
 magnetic field of one tesla is very powerful magnetic field. </span><span
 style=3D'position:absolute;top:79.75%;left:7.67%;width:94.0%;height:5.25%'=
>Sometimes
 it may be convenient to use the gauss, which is </span><span style=3D'posi=
tion:
 absolute;top:85.0%;left:7.67%;width:91.76%;height:5.25%'>equal to 1/10,000=
 of
 a tesla. Earth&#8217;s magnetic field, at the </span><span style=3D'positi=
on:
 absolute;top:90.25%;left:7.67%;width:87.26%;height:5.25%'>surface, varies =
but
 has the strength of about one gauss.</span></div>
 <div v:shape=3D"_x0000_s8200" class=3DO style=3D'mso-line-spacing:"100 50 =
0";
 position:absolute;top:32.25%;left:9.36%;width:51.49%;height:7.75%'><span
 style=3D'font-family:Arial;font-size:150%;color:#000099'>1</span><span
 style=3D'font-family:Arial;color:#000099'> </span><span style=3D'font-fami=
ly:Arial;
 font-size:150%;color:#000099'>N =3D 1</span><span style=3D'font-family:Ari=
al;
 font-size:83%;color:#000099'> </span><span style=3D'font-family:Arial;
 font-size:150%;color:#000099'>C</span><span style=3D'font-family:Arial;
 font-size:67%;color:#000099'> </span><span style=3D'font-family:Arial;
 font-size:150%;color:#000099'>(m</span><span style=3D'font-family:Arial;
 font-size:33%;color:#000099'> </span><span style=3D'font-family:Arial;
 font-size:150%;color:#000099'>/</span><span style=3D'font-family:Arial;
 font-size:33%;color:#000099'> </span><span style=3D'font-family:Arial;
 font-size:150%;color:#000099'>s)</span><span style=3D'font-family:Arial;
 font-size:50%;color:#000099'> </span><span style=3D'font-family:Arial;
 font-size:150%;color:#000099'>(T)</span><span style=3D'font-family:Arial;
 font-size:150%;color:#000099;mso-special-format:lastCR;display:none'>&#13;=
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 <div v:shape=3D"_x0000_s8201" class=3DO style=3D'mso-line-spacing:"100 50 =
0";
 position:absolute;top:18.25%;left:11.79%;width:78.08%;height:8.5%'><span
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 style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>q</i></span><span
 style=3D'font-family:Arial;font-size:50%;color:red'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
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 style=3D'font-family:Arial;font-size:50%;color:red'><i><span
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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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d'><i>B</i></span><span
 style=3D'font-family:Arial;font-size:50%;color:red'><i><span
 style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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d'>sin</span><span
 style=3D'font-family:Symbol;mso-ascii-font-family:Arial;font-size:150%;
 color:red;mso-char-type:symbol'><i>q</i></span><span style=3D'font-family:=
Arial;
 font-size:150%;color:red'><i><span style=3D'mso-spacerun:yes'>&nbsp; </spa=
n></i></span></div>
 <div v:shape=3D"_x0000_s8202" class=3DO style=3D'mso-line-spacing:"100 50 =
0"'><span
 style=3D'position:absolute;top:42.0%;left:4.3%;width:101.12%;height:5.25%'=
>From
 the formula for magnetic force we can find a relationship </span><span
 style=3D'position:absolute;top:47.5%;left:4.3%;width:102.8%;height:5.25%'>=
between
 the tesla and other SI units. The sine of an angle has no </span><span
 style=3D'position:absolute;top:52.75%;left:4.3%;width:92.32%;height:5.25%'=
>units,
 so </span></div>
 <div v:shape=3D"_x0000_s8203" class=3DO style=3D'mso-line-spacing:"100 50 =
0";
 position:absolute;top:57.25%;left:22.65%;width:15.73%;height:7.75%'><span
 style=3D'font-family:Arial;font-size:150%;color:#000099'>1</span><span
 style=3D'font-family:Arial;color:#000099'> </span><span style=3D'font-fami=
ly:Arial;
 font-size:150%;color:#000099'>T =3D </span><span style=3D'font-family:Aria=
l;
 font-size:150%;color:#000099;mso-special-format:lastCR;display:none'>&#13;=
</span></div>
 <div v:shape=3D"_x0000_s8204" class=3DO style=3D'mso-line-spacing:"100 50 =
0";
 position:absolute;top:53.25%;left:40.26%;width:15.73%;height:7.75%'><span
 style=3D'font-family:Arial;font-size:150%;color:#000099'>1</span><span
 style=3D'font-family:Arial;color:#000099'> </span><span style=3D'font-fami=
ly:Arial;
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pan></span><span
 style=3D'font-family:Arial;font-size:150%;color:#000099;mso-special-format=
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 position:absolute;top:53.25%;left:64.41%;width:15.73%;height:7.75%'><span
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pan></span><span
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 position:absolute;top:62.25%;left:64.41%;width:12.35%;height:7.75%'><span
 style=3D'font-family:Arial;font-size:150%;color:#000099'>A</span><span
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  <v:shadow color=3D"gray [2]"/>
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 src=3D"slide0047_image026.gif" style=3D'position:absolute;top:57.49%;left:=
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 width:13.1%;height:10.25%'><![endif]>
 <div v:shape=3D"_x0000_s75779" class=3DT style=3D'position:absolute;top:5.=
25%;
 left:8.42%;width:83.33%;height:6.75%'><span style=3D'font-family:Westminst=
er'>Direction
 of Magnetic Field &amp; Force</span></div>
 <div v:shape=3D"_x0000_s75780" class=3DO style=3D'mso-line-spacing:"100 50=
 0"'><span
 style=3D'position:absolute;top:22.0%;left:9.36%;width:79.77%;height:5.25%'=
><span
 style=3D'mso-special-format:lastCR;display:none'>&#13;</span></span></div>
 <div v:shape=3D"_x0000_s75793" class=3DO style=3D'mso-line-spacing:"100 50=
 0";
 position:absolute;top:65.25%;left:42.69%;width:5.61%;height:6.0%'><span
 style=3D'font-family:Arial;font-size:117%;color:#006600'><b><i>B</i></b></=
span></div>
 <div v:shape=3D"_x0000_s75794" class=3DO style=3D'text-align:center;positi=
on:absolute;
 top:57.49%;left:55.99%;width:2.43%;height:5.25%'><span style=3D'color:red'=
><b>+</b></span></div>
 <div v:shape=3D"_x0000_s75795" class=3DO style=3D'mso-line-spacing:"100 50=
 0"'><span
 style=3D'position:absolute;top:13.25%;left:2.62%;width:108.98%;height:4.25=
%'><span
 style=3D'font-size:83%'>Near the poles, where the field lines are close
 together, the field is very strong (so </span></span><span style=3D'positi=
on:
 absolute;top:17.5%;left:2.62%;width:106.92%;height:4.25%'><span
 style=3D'font-size:83%'>the field vector are drawn longer). Anywhere in the
 field the mag. field vector is </span></span><span style=3D'position:absol=
ute;
 top:22.0%;left:2.62%;width:108.98%;height:4.25%'><span style=3D'font-size:=
83%'>always
 tangent to the mag. field line there. The </span><span style=3D'font-size:=
83%'><b>+</b></span><span
 style=3D'font-size:83%'> charge in the pic in moving into </span></span><s=
pan
 style=3D'position:absolute;top:26.5%;left:2.62%;width:98.12%;height:5.25%'=
><span
 style=3D'font-size:83%'>the page. Since<span style=3D'mso-spacerun:yes'>&n=
bsp;
 </span></span><span style=3D'font-family:Arial;font-size:83%'><i>q</i></sp=
an><span
 style=3D'font-size:83%'><span style=3D'mso-spacerun:yes'>&nbsp; </span>is =
+, the </span><span
 style=3D'font-family:Arial;font-size:83%'><i>q</i></span><span style=3D'fo=
nt-family:
 Arial;font-size:42%'><i> </i></span><span style=3D'font-family:Arial;font-=
size:
 83%'><b><i>v</i></b></span><span style=3D'font-size:83%'> vector is also i=
nto
 the page. The<span style=3D'mso-spacerun:yes'>&nbsp; </span></span>-<span
 style=3D'font-size:83%'><span style=3D'mso-spacerun:yes'>&nbsp; </span>cha=
rge
 <br>
  </span></span><span style=3D'position:absolute;top:31.75%;left:2.62%;
 width:103.18%;height:4.5%'><span style=3D'font-size:83%'>is moving to the =
right,
 so the </span><span style=3D'font-family:Arial;font-size:83%'><i>q</i></sp=
an><span
 style=3D'font-family:Arial;font-size:42%'><i> </i></span><span style=3D'fo=
nt-family:
 Arial;font-size:83%'><b><i>v</i></b></span><span style=3D'font-size:83%'> =
vector
 is to the left. The mag. force vector is </span></span><span style=3D'posi=
tion:
 absolute;top:36.0%;left:2.62%;width:94.0%;height:4.75%'><span
 style=3D'font-size:83%'>always </span><span style=3D'font-family:Symbol;
 font-size:83%;mso-char-type:symbol'>^</span><span style=3D'font-size:83%'>=
 to
 plane formed by the </span><span style=3D'font-family:Arial;font-size:83%'=
><i>q</i></span><span
 style=3D'font-family:Arial;font-size:42%'><i> </i></span><span style=3D'fo=
nt-family:
 Arial;font-size:83%'><b><i>v</i></b></span><span style=3D'font-size:83%'> =
vector
 and the </span><span style=3D'font-family:Arial;font-size:83%'><b><i>B</i>=
</b></span><span
 style=3D'font-size:83%'> vector. </span></span></div>
 <v:oval id=3D"_x0000_s75796" style=3D'position:absolute;left:546pt;top:304=
.25pt;
  width:24pt;height:24pt;mso-wrap-style:none;v-text-anchor:middle' fillcolo=
r=3D"white [0]"
  strokecolor=3D"#009" strokeweight=3D"2.25pt">
  <v:shadow color=3D"gray [2]"/>
 </v:oval><v:line id=3D"_x0000_s75797" style=3D'position:absolute;flip:y' f=
rom=3D"566.875pt,198pt"
  to=3D"646.25pt,304.25pt" strokecolor=3D"#060" strokeweight=3D"2.25pt">
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=3D"#0c9 [4]"
  stroked=3D"f" strokecolor=3D"black [1]">
  <v:fill color2=3D"white [0]"/>
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 </v:shape><v:shape id=3D"_x0000_s75799" type=3D"#_x0000_t202" style=3D'pos=
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  left:542.875pt;top:284.75pt;width:42pt;height:55.25pt' filled=3D"f"
  fillcolor=3D"#0c9 [4]" stroked=3D"f" strokecolor=3D"#009">
  <v:fill color2=3D"white [0]"/>
  <v:shadow color=3D"gray [2]"/>
  <v:textbox style=3D'mso-fit-shape-to-text:t'/>
 </v:shape><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s75796,_x0000_s75=
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 src=3D"slide0047_image027.gif" style=3D'position:absolute;top:36.0%;left:7=
5.65%;
 width:14.98%;height:25.25%'><![endif]>
 <div v:shape=3D"_x0000_s75796" class=3DO style=3D'text-align:center'><span
 style=3D'position:absolute;top:56.25%;left:77.15%;width:.93%;height:5.25%'=
><span
 style=3D'color:red;mso-special-format:lastCR;display:none'><b>&#13;</b></s=
pan></span></div>
 <div v:shape=3D"_x0000_s75798" class=3DO style=3D'mso-line-spacing:"100 50=
 0";
 position:absolute;top:38.75%;left:88.57%;width:5.61%;height:6.0%'><span
 style=3D'font-family:Arial;font-size:117%;color:#006600'><b><i>B</i></b></=
span></div>
 <div v:shape=3D"_x0000_s75799" class=3DO style=3D'mso-line-spacing:"100 50=
 0";
 position:absolute;top:54.0%;left:76.4%;width:3.93%;height:8.5%'><span
 style=3D'font-size:167%;color:#000099'>-</span></div>
 <v:line id=3D"_x0000_s75800" style=3D'position:absolute' from=3D"570pt,318=
pt" to=3D"684pt,318pt"
  strokecolor=3D"red" strokeweight=3D"2.25pt">
  <v:stroke endarrow=3D"block"/>
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 </v:line><v:shape id=3D"_x0000_s75801" type=3D"#_x0000_t202" style=3D'posi=
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  left:678pt;top:312pt;width:54pt;height:40.875pt' filled=3D"f" fillcolor=
=3D"#0c9 [4]"
  stroked=3D"f" strokecolor=3D"black [1]">
  <v:fill color2=3D"white [0]"/>
  <v:shadow color=3D"gray [2]"/>
  <v:textbox style=3D'mso-fit-shape-to-text:t'/>
 </v:shape><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s75800"
 src=3D"slide0047_image028.gif" style=3D'position:absolute;top:57.99%;left:=
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 width:16.47%;height:2.25%'><![endif]>
 <div v:shape=3D"_x0000_s75801" class=3DO style=3D'mso-line-spacing:"100 50=
 0";
 position:absolute;top:58.75%;left:95.13%;width:5.61%;height:6.0%'><span
 style=3D'font-family:Arial;font-size:117%;color:red'><b><i>v</i></b></span=
></div>
 <v:line id=3D"_x0000_s75802" style=3D'position:absolute;flip:x y' from=3D"=
366pt,246pt"
  to=3D"402pt,312pt" strokecolor=3D"#009" strokeweight=3D"3pt">
  <v:stroke endarrow=3D"block"/>
  <v:shadow color=3D"gray [2]"/>
 </v:line><v:shape id=3D"_x0000_s75803" type=3D"#_x0000_t202" style=3D'posi=
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  left:372pt;top:228pt;width:54pt;height:40.875pt' filled=3D"f" fillcolor=
=3D"#0c9 [4]"
  stroked=3D"f" strokecolor=3D"black [1]">
  <v:fill color2=3D"white [0]"/>
  <v:shadow color=3D"gray [2]"/>
  <v:textbox style=3D'mso-fit-shape-to-text:t'/>
 </v:shape><v:shape id=3D"_x0000_s75804" type=3D"#_x0000_t202" style=3D'pos=
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  left:12pt;top:240pt;width:294pt;height:252pt' filled=3D"f" fillcolor=3D"#=
0c9 [4]"
  stroked=3D"f" strokecolor=3D"black [1]">
  <v:fill color2=3D"white [0]"/>
  <v:shadow color=3D"gray [2]"/>
  <v:textbox style=3D'mso-fit-shape-to-text:t'/>
 </v:shape><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s75802"
 src=3D"slide0047_image029.gif" style=3D'position:absolute;top:44.75%;left:=
50.0%;
 width:6.36%;height:13.75%'><![endif]>
 <div v:shape=3D"_x0000_s75803" class=3DO style=3D'mso-line-spacing:"100 50=
 0";
 position:absolute;top:43.25%;left:52.62%;width:5.61%;height:6.0%'><span
 style=3D'font-family:Arial;font-size:117%;color:#000099'><b><i>F</i></b></=
span></div>
 <div v:shape=3D"_x0000_s75804" class=3DO style=3D'mso-line-spacing:"100 50=
 0"'><span
 style=3D'position:absolute;top:45.5%;left:2.62%;width:44.75%;height:5.25%'=
><span
 style=3D'font-size:83%'>The force on the<span style=3D'mso-spacerun:yes'>&=
nbsp;
 </span></span>-<span style=3D'font-size:83%'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>charge is into </span></span><span
 style=3D'position:absolute;top:50.74%;left:2.62%;width:45.5%;height:4.25%'=
><span
 style=3D'font-size:83%'>the page. If a charge is motionless </span></span>=
<span
 style=3D'position:absolute;top:55.25%;left:2.62%;width:40.82%;height:4.25%=
'><span
 style=3D'font-size:83%'>relative to the field, there is no </span></span><=
span
 style=3D'position:absolute;top:59.5%;left:2.62%;width:46.44%;height:4.25%'=
><span
 style=3D'font-size:83%'>magnetic force on it, but if either a </span></spa=
n><span
 style=3D'position:absolute;top:64.0%;left:2.62%;width:42.69%;height:4.25%'=
><span
 style=3D'font-size:83%'>magnet is moving or a charge is </span></span><span
 style=3D'position:absolute;top:68.5%;left:2.62%;width:45.88%;height:4.25%'=
><span
 style=3D'font-size:83%'>moving, there could a force on the </span></span><=
span
 style=3D'position:absolute;top:73.0%;left:2.62%;width:45.31%;height:4.25%'=
><span
 style=3D'font-size:83%'>charge. If a charge moves parallel </span></span><=
span
 style=3D'position:absolute;top:77.25%;left:2.62%;width:40.63%;height:4.25%=
'><span
 style=3D'font-size:83%'>to a magnetic field, there is no </span></span><sp=
an
 style=3D'position:absolute;top:81.75%;left:2.62%;width:38.95%;height:4.25%=
'><span
 style=3D'font-size:83%'>magnetic force on it, since<span
 style=3D'mso-spacerun:yes'>&nbsp; </span><br>
  </span></span><span style=3D'position:absolute;top:86.25%;left:2.62%;
 width:38.95%;height:4.25%'><span style=3D'font-size:83%'>sin</span><span
 style=3D'font-size:67%'> </span><span style=3D'font-size:83%'>0</span><span
 style=3D'font-family:"Times New Roman";mso-bidi-font-family:"Times New Rom=
an";
 font-size:83%'>&deg;</span><span style=3D'font-size:83%'><span
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size:83%;
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